Answers by Arkaprava / GATE Overflow for GATE CSE

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41

Michael Sipser Edition 3 Exercise 0 Question 11 (Page No. 27)
Let $S(n) = 1 + 2 + · · · + n$ be the sum of the first $n$ natural numbers and let $C(n) = 1^{3} + 2^{3} + · · · + n^{3}$ be the sum of the first $n$ cubes. Prove the following equalities by induction on $n,$ ... $C(n)=\frac{1}{4}(n^{4}+2n^{3}+n^{2}=\frac{1}{4}n^{2}(n+1)^{2}.$

Let $S(n) = 1 + 2 + · · · + n$ be the sum of the first $n$ natural numbers and let $C(n) = 1^{3} + 2^{3} + · · · + n^{3}$ be the sum of the first $n$ cubes. Prove t...

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answered May 8, 2019

1 votes

42

Michael Sipser Edition 3 Exercise 1 Question 11 (Page No. 85)
Prove that every $\text{NFA}$ can be converted to an equivalent one that has a single accept state.

Prove that every $\text{NFA}$ can be converted to an equivalent one that has a single accept state.

1.1k views

answered May 8, 2019

2 votes

43

GATE2016 EC-2: GA-5
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have $6$ hour shifts in a day, whereas E and F have $12$ hours shifts. What is the ratio of contribution of M to contribution of E in the project? $1:1$ $1:2$ $1:4$ $2:1$

S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have $6$ hou...

4.6k views

answered May 8, 2019

3 votes

44

ISI2019-MMA-10
The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the student is told that he has been admitted to at least one of these colleges, what is the probability that he has got admitted to college $A$? $3/5$ $5/7$ $10/13$ $15/19$

The chance of a student getting admitted to colleges $A$ and $B$ are $60\%$ and $40\%$, respectively. Assume that the colleges admit students independently. If the studen...

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answered May 6, 2019

3 votes

45

ISI2019-MMA-9
$(\cos 100^\circ + i \sin 100^\circ)(\cos 0^\circ + i \sin 110^\circ)$ is equal to $\frac{1}{2}(\sqrt3 – i)$ $\frac{1}{2}(-\sqrt3 – i)$ $\frac{1}{2}(-\sqrt3 +i)$ $\frac{1}{2}(\sqrt3 + i)$

$(\cos 100^\circ + i \sin 100^\circ)(\cos 0^\circ + i \sin 110^\circ)$ is equal to$\frac{1}{2}(\sqrt3 – i)$$\frac{1}{2}(-\sqrt3 – i)$$\frac{1}{2}(-\sqrt3 +i)$$\frac{...

1.1k views

answered May 6, 2019

1 votes

46

MadeEasy Subject Test 2019: Combinatory - Permutations And Combinations
Q.The number of ways, we can arrange 5 books in 3 shelves ________.

Q.The number of ways, we can arrange 5 books in 3 shelves ________.

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answered Mar 25, 2019

0 votes

47

Model Question IISc CDS CS Written Test Sample question
Anand is preparing a pizza with 8 slices, and he has 10 toppings to put on the pizza. He can put only one topping on each slice but can use the same topping on zero or more slices. In how many unique ways can he prepare the slices so that the same topping is not used in adjacent slices?

Anand is preparing a pizza with 8 slices, and he has 10 toppings to put on the pizza. He can put only onetopping on each slice but can use the same topping on zero or mor...

1.8k views

answered Mar 15, 2019

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